It is known that fuel injection into a cylinder of an internal combustion engine is carried out by being divided into a plurality of injections. With this, combustion can be promoted by carrying out an after or post injection after a main injection, so that smoke can be reduced or fuel economy can be improved. Here, there have been known a technique of making a change of an injection rate of fuel (an amount of injection of fuel per unit time) from a fuel injection valve in an initial or early injection stage of a post injection larger than that of a main injection, and a technique of changing an injection rate of fuel by making the speed of a needle in a fuel injection valve at the time of a post injection higher than that at the time of a main injection (for example, refer to a first patent literature). In these techniques, a penetration force of fuel at the time of the post injection is made large.